Fairy tale composition

King of the forest
One day, the lion went to the lake to drink water. Seeing his old face, he sighed: "Alas, it's time for me, the king of the forest," said the lion
The next day, the lion told everyone, "every animal takes turns to be the king of the forest, and each animal will be the king of the forest for ten days. Let the one who is good at it be the king of the forest."
The first one is the tiger. The tiger ordered: "every animal has to learn how to bark from me every day and night." ten days later, the animals are hoarse
The second mouse, it ordered: "from today on, every animal can only live in the cave and steal at night." ten days later, the black circles of the animals came out
The third one was kangaroo, who immediately ordered: "every animal is jumping like me." ten days passed, and the animals were exhausted
The fourth is the bird. The animals all think: will they fly in the sky and live in the bird's nest every day? The bird says: "every animal has its own life." the following cheers. The lion says: "no wheels, the bird is the king of the forest!"
The mouse, tiger and kangaroo were not reconciled. The mouse yelled, "why can the bird be the king of the forest? We have many advantages!" the tiger and kangaroo also said one after another, "that's right. We have many advantages." the lion said, "do you think the animals are happy soon?" the mouse stammered, "well, it's not our fault, They are too stupid! "The bird retorted:" it's not that they are too stupid, but that you are too hateful. Every animal has its own life. For example, swallows don't go to cold places, but polar bears like cold places! "The animals also coaxed:" it's absolutely right to choose birds as the king of the forest! "Finally, the bird became the king of the forest

Guess whether the square difference of two consecutive odd numbers is a mysterious number? Please give an example

The square difference of two adjacent odd numbers must be divisible by 8
Let an odd number be 2N-1
The other is 2n + 1.. (n is an integer)
(2n+1)^2-(2n-1)^2=4n^2+4n+1-(4n^2-4n+1)
=8n
∵ n is an integer
8 N is divisible by 8

To make a rectangular frame with a bottom area of 36 square centimeters and a height of 4.5 centimeters, at least how many centimeters of iron wire do you need?

36=6×6
At least = 4 × (6 + 6 × 4.5) = 66 cm

English translation
And it's 7:10 in the morning. It's time to get up and on weekdays. Parents are busy, but they are free on weekends
These three sentences start with 10
Fractional total pair

What time is your performance?
What time is it on your watch
It's 7:10 in the morning
It's ten past seven in the morning now.
It's time to get up
It's time to get up.
Parents are busy on weekdays, but they are free on weekends
Parents are busy on workday,but they are free on weekend.

Circle C: x2 + Y2 + 4ax + 4a2-4 = 0 and circle C: x2 + y2-2by + b2-1 = 0 have only one common tangent. If a ∈ R, B ∈ R and ab ≠ 0, then the minimum value of 1 / A2 + 1 / B2 is 0
A.2
B.4
C.8
D.9

The answer: the minimum value of 9, the minimum value of 9, the D, the D, the D, the D, the D, the D, the minimum value of 9, the minimum value of 9, the D, the D, the first, the formula of the two round equations, the formula x-178; + y-178; + y-178; + y-178; - 4b-1 + 4B (##178; - 4bby-1-1 + 4B and##178; = x-178; (x-178; + x-178; + (y-2b); (y-2b); \35\\\\#178; (y-2b); (0,2b) is the center of (0,2b) as (0,2b) as the center of (0,2b) and the center of (0,2b) as the center of the circle, the center of (0,2b) and the center of the center of X & #

Let a and B be two nonzero vectors. It is proved that a and B are collinear if and only if a + B and A-B are collinear

It is proved that if a and B are collinear, then a = M B a + B = (M + 1) B A-B = (m-1) B, that is, a + B = (M + 1) / (m-1) (a-b), that is, a + B and A-B are collinear
If a + B A-B is collinear, then a + B = n (a-b) = n a-N B, (n-1) a = (n + 1) B, that is, a = (n + 1) / (n-1) B is collinear
In conclusion, a and B are collinear if and only if a + B and A-B are collinear

As shown in the figure, in the triangle ABC, ab = AC, the angle BAC = 120 °, the vertical bisector EF of AC intersects AC at point E, BC at point E, BC at point F
BC=3FC

Proof: connect AF
∵AB＝AC,∠BAC＝120
∴∠B＝∠C＝（180-∠BAC）/2＝30
∵ EF vertical split AC
∴AF＝CF
∴∠CAF＝∠C＝30
∴∠BAF＝∠BAC-∠CAF＝90
∴BF＝2AF
∴BF＝2CF
∴BC＝BF+CF＝3CF

Let f (x) = 2x cosx, {an} be an arithmetic sequence with tolerance of π / 8, f (A1) + F (A2) + If f (A5) = 5 π, then [f (a)] ^ 2-A2 * A3=

This is the 2012 Sichuan college entrance examination question 12, I did it right at that time
Almost all of them have typed a1a5 as a1a3 on the Internet

Because f (A1) + F (A2) + F (A3) + F (A4) + F (A5) = 5 π, f (x) = 2x cosx

SO 2 (a1 + A2 + a3 + A4 + A5) - (cosa1 + cosa2 + cosa3 + cosa4 + cosa5) = 5 π

SO 2 (a1 + A2 + a3 + A4 + A5) = 5 π

Because {an} is an arithmetic sequence

So 10a3 = 5 π

So A3 = π / 2

So f (A3) = π

Because the tolerance of {an} is π / 8

So a1a5 = (A3 - π / 4) (A3 + π / 4) = (π / 4) (3 π / 4) = 3 π & # / 16

So [f (A3)] ² - a1a5 = π & #178; - 3 π & #178 / 16 = 13 π & #178 / 16

So the answer is d

Space vector... Coplanar four points
For four coplanar points, if the equation XPA + ypb + ZPC = 0 (PA, Pb, PC, 0 are all vectors), whether there must be x + y + Z = 1, and vice versa

If both sides of the equation multiply a at the same time, we get axpa + aypb + azpc = 0, then ax + ay + AZ = 1, but x + y + Z = 1 instead of 1 / A

In the triangle ABC, the angle ACB is 90 degrees, the point D.E is the midpoint of AC and ab respectively, and the extension line of BF / / CE intersection De is at F
In a hurry
It was deleted in 15 minutes
Finding out whether a quadrilateral cefb is a parallelogram

Delete in 15 minutes, so many symbols are more than 15 minutes
I'll make it simple. You can think about it yourself
Triangle ade is similar to triangle ACB, so De is parallel to CB, that is, EF is parallel to CB
Because CE is parallel to BF
The two opposite sides are parallel to each other, so the quadrilateral cefb is a parallelogram

Fairy tale composition